CN104835319A - Method for estimating vehicle import behavior on high-grade road bottleneck zone on-ramp - Google Patents

Abstract

The invention discloses a method for estimating vehicle import behavior on a high-grade road (highway and city expressway) bottleneck zone on-ramp. The method uses a hidden Markov model to estimate decision conditions of a driver in an import process. The method comprises five steps of a data preparation stage, a data preprocessing stage, a model learning stage, a model decoding stage, and a result processing stage. The method can estimate states of a vehicle at different time before importing to a high-grade road main line. An estimated state time sequence can reflect the decision process of a driver. The method analyzes driver state transition spatial distribution conditions, so as to find out frequent places and zones where the drivers have lane changing intention. Therefore, the method provides basis for designing and developing an efficient on-ramp bottleneck zone lane-changing assistance system, and provides important reference for measure design for preventing early-onset failure of high-grade road on-ramp bottleneck.

Description

A kind of advanced road bottle-neck zone enters ring road vehicle and imports behavior method of estimation

Technical field

The present invention relates to a kind of method for advanced road traffic behavior identification field, in particular, the present invention relates to a kind of advanced road bottle-neck zone based on Hidden Markov Model (HMM) and enter ring road vehicle remittance behavior method of estimation.

Background technology

Advanced road (highway and city expressway) enters the normal area that ring road bottleneck is traffic jam, security incident.The remittance behavior entering ring road vehicle is then one of major reason causing bottleneck to lose efficacy.Relevant scholar controls from speed limit, setting fixing remittance section, signal the validity angularly inquiring into the improvement of this phenomenon mostly.So far, some scholars has adopted some sorting algorithms to be identified driving behavior state, but, seldom there is scholar to analyze the mechanism that driver imports behavior decision process and behind.Behavior state before the present invention successfully can import driver carries out the estimation of many moment point thus reflects the whole decision process of driver more comprehensively.Driver can be obtained furtherly when state transfer, the number of times of vehicle-state transfer and the traffic flow modes information of both macro and micro corresponding to this moment occur.

Hidden Markov Model (HMM) completes study and decoding two processes by remittance vehicle observable state set and 3 initial matrixs according to certain algorithm.Learning phase adopts forward-backward algorithm algorithm, and recurrence obtains the locally optimal solution of Hidden Markov Model (HMM) inner parameter.Decode phase adopts Viterbi algorithm, is obtained the state estimation time series of each remittance vehicle the best in some sense by iteration.

Summary of the invention

The object of the present invention is to provide a kind of advanced road bottle-neck zone to enter ring road vehicle and import behavior method of estimation, successfully import the whole decision process before advanced road main line to resolve driver, calculate decision point and corresponding states information and then obtain the decision-making mechanism that driver imports behavior that driver imports.The present invention not only can enter the exploitation of ring road bottle-neck zone lane-changing assistance system efficiently and provides foundation for designing, and can enter ring road bottleneck early onset inefficacy Measure Design and provide important references for prevention advanced road.

A kind of advanced road bottle-neck zone vehicle of the present invention imports behavior method of estimation, comprises the following steps:

(1) data preparation stage: first utilize trajectory extraction software to carry out the extraction of track of vehicle data, then establishes the traffic stream characteristics index set affecting remittance behavior;

(1.1) utilize trajectory extraction software to carry out the extraction of track of vehicle data, the track data of vehicle comprises the ID of vehicle, moment, the speed of vehicle, the acceleration of vehicle, and the position coordinates of vehicle;

(1.2) establish the traffic stream characteristics index set C affecting remittance behavior, described traffic stream characteristics index set C comprises the speed V importing vehicle, the acceleration a importing vehicle, imports the time headway T of Adjacent vehicles (front truck, rear car) on vehicle-to-target track _leadand T _lag, import the headstock Ullage S of Adjacent vehicles (front truck, rear car) on vehicle-to-target track _leadand S _lag, import the time headway T of adjacent front truck on vehicle and current lane _prewith headstock Ullage S _pre, import the velocity contrast Δ V of Adjacent vehicles (front truck, rear car) on vehicle-to-target track _leadwith Δ V _lag, and import the position coordinates D of vehicle relative acceleration lane tail end;

(2) data preprocessing phase: this stage comprise traffic stream characteristics index set C data acquisition, import the identification of behavior characteristic variable n, determine the structure R of driving behavior state matrix Q, observable state set, and obtain 3 initial matrixs that originally Hidden Markov Model (HMM) need to input;

(2.1) data acquisition of traffic stream characteristics index set C, according to trajectory extraction software obtain vehicle ID, the moment, the speed of vehicle, the acceleration of vehicle, and the location coordinate information data of vehicle, by indirect calculation obtain Ullage, time apart from, velocity contrast;

Ullage: the Ullage before and after a certain moment between adjacent two cars equals front vehicle position coordinate and deducts the vehicle commander that rear car position coordinates deducts rear car again, unit m;

Time distance: the Ullage before and after current time between adjacent two cars divided by rear car current vehicle speed, unit s;

Velocity contrast: the automobile's instant velocity of current time front truck deducts the speed of a motor vehicle of contiguous rear car, unit m/s;

Vehicle commander's computation rule: compact car 4.5m, in-between car 6.0m, large car 12.0m;

(2.2) import the identification of behavior characteristic variable n, adopt random forests algorithm to be screened the traffic stream characteristics index set affecting remittance behavior, obtain the characteristic variable affecting remittance behavior; Described characteristic variable comprise import vehicle acceleration a, import headstock Ullage S between vehicle-to-target track front truck _lead, import time headway T between vehicle-to-target track front truck _lead, import headstock Ullage S between vehicle-to-target track rear car _lag, import velocity contrast Δ V between vehicle-to-target track front truck _lead, and import the velocity contrast Δ V between the rear car of vehicle-to-target track _lag, characteristic variable n as shown in the formula:

n＝(a，S _lead，T _lead，S _lag，ΔV _lead，ΔV _lag)

In formula: a---import the acceleration of vehicle, unit is m/s ²;

S _lead---import the headstock Ullage between the front truck of vehicle-to-target track, unit is m;

T _lead---import the time headway between the front truck of vehicle-to-target track, unit is s;

S _lag---import the headstock Ullage between the rear car of vehicle-to-target track, unit is m;

Δ V _lead---import the velocity contrast between the front truck of vehicle-to-target track, unit is m/s;

Δ V _lag---import the velocity contrast between the rear car of vehicle-to-target track, unit is m/s;

(2.3) determine driving behavior state matrix Q, described state comprises bottle-neck zone and enters the state (remittance state) of ring road vehicle remittance main line and enter ring road vehicle along the normal transport condition of acceleration lane (non-remittance state).

Q＝{q ₁，q ₂}

In formula: q ₁---enter ring road vehicle and import state, represent by numeral 1;

Q ₂---enter ring road vehicle and do not import state, represent by numeral 2;

(2.4) structure of observable state set R, the characteristic variable that step (2.2) obtains is sextuple, and each dimension variable is continuous variable; Owing to needing to carry out sliding-model control to characteristic variable when building Hidden Markov Model (HMM), therefore the interval division such as employing are by a, S _lead, T _lead, S _lag, Δ V _lead, Δ V _lagbe divided into k class, l class, p class, s class, h class and z class respectively; As mentioned above, the observable state set R that element number is k × l × p × s × h × z can finally be obtained, with two dimensional feature vector (S _lead, a) for example illustrates the mode that embodies of observable state set, its mathematical form is as follows:

$\begin{array}{c}R=\{R_{11},...,R_{1j},...,R_{i1},R_{\mathrm{ij}}\}\\ =\left\{\begin{array}{c}(S_{{\mathrm{lead}}_1},a_1),(S_{{\mathrm{lead}}_1},a_2),...,(S_{{\mathrm{lead}}_1},a_k)\\ (S_{{\mathrm{lead}}_2},a_1),({S_{{\mathrm{lead}}_2}}_{},a_2),...,(S_{{\mathrm{lead}}_2},a_k)\\ ......\\ (S_{{\mathrm{lead}}_l},a_1),(S_{{\mathrm{lead}}_l},a_2),...,(S_{{\mathrm{lead}}_l},a_k)\end{array}\right\}\end{array}$

In formula: R _ij---observable state;

A---import the acceleration of vehicle, unit is m/s ²;

S _lead---import the headstock Ullage between the front truck of vehicle-to-target track, unit is m;

L---import the headstock Ullage S between the front truck of vehicle-to-target track _leadaccording to etc. the interval number of interval division;

K---the acceleration a importing vehicle according to etc. the interval number of interval division;

(2.5) obtain 3 initial matrixs that originally Hidden Markov Model (HMM) needs to input, described initial matrix is state transition probability matrix A, observed value probability distribution matrix B and initial state probabilities distribution matrix π respectively;

State transition probability matrix A: state transition probability matrix reflection be that under the prerequisite determined of ring road vehicle previous moment state, subsequent time is certain shape probability of state.As described above obtains the matrix A of 2 × 2, and its mathematical form is as follows:

a _ij＝P(Q _t＝q _j|Q _t-1＝q _i)，i，j＝1 or 2

$A=\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]$

In formula: a _ij---enter ring road vehicle and transfer to another kind of shape probability of state from a kind of state;

A ₁₁---previous moment is remittance state, and a rear moment is for importing shape probability of state;

A ₁₂---previous moment is remittance state, and a rear moment is non-remittance shape probability of state;

A ₂₁---previous moment is non-remittance state, and a rear moment is for importing shape probability of state;

A ₂₂---previous moment is non-remittance state, and a rear moment is non-remittance shape probability of state;

Observed value probability distribution matrix B: it reflects that ring road vehicle (imports or non-remittance) under certain hidden state and is considered to certain observable shape probability of state.Still with two dimensional feature vector (S _lead, a) for example illustrates the form that embodies of observed value probability distribution matrix, its mathematical form is as follows:

b _ij＝P(O _t＝R _ij|Q _t＝q _i)，i＝1 or 2，j＝1，2，…，m

$B=\left[\begin{array}{ccc}{b}_{11}& ...& b_{1m}\\ b_{21}& & b_{2m}\end{array}\right]$

m＝l*k

In formula: b _ij---driver is considered to certain observable shape probability of state under a certain hidden state;

M---all observe the division number of proper vector, the implication of l and k is the same;

Initial state probabilities distribution matrix π: implicit state (importing and the non-remittance) probability distribution matrix when initial time t=1, its mathematical form is as follows:

π＝{π ₁，π ₂}

π ₁＝P ₀(Q _t＝1＝q ₁)

π ₂＝P ₀(Q _t＝1＝q ₂)

In formula: π ₁---during initial time t=1, enter ring road vehicle for importing shape probability of state;

π ₂---during initial time t=1, entering ring road vehicle is non-remittance shape probability of state;

(3) the model learning stage: the initial parameter λ to be optimized that can obtain model through data preparation stage and data preprocessing phase ₀, λ ₀=(π, A, B).The model learning stage adopts forward-backward algorithm algorithm constantly to reappraise the parameter lambda of model ₀, after successive ignition, obtain a local optimum parametric solution of model thus provide important leverage for the realization of following model decode phase; Specific implementation step is as follows:

(3.1) forwards algorithms: establish observable state for time sequence O=(O ₁, O ₂..., O _t), O to represent in a vehicle travel process not observable state (characteristic variable value) in the same time, and definition forward variable is:

α _t(i)＝P(O ₁，O ₂，…，O _t，Q _t＝q _i|λ)，1≤t≤T

In formula: α _t(i)---the probability of t hidden state i;

(3.1.1) start

α ₁(i)＝π _ib(O ₁)，t＝1

In formula: b (O ₁)---initial time observer state is O ₁probability;

(3.1.2) recurrence

${\mathrm{\α}}_{t+1}\left(j\right)=\left[\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_t\left(i\right)a_{\mathrm{ij}}\right]b_{{\mathrm{jO}}_{t+1}},1\≤t\≤T-\mathrm{1,1}\≤j\≤N$

In formula: α _t+1j ()---t+1 moment state is the probability of j;

---when hidden state is j, observer state is O _t+1probability;

(3.1.3) terminate

$P\left(O\right|\mathrm{\λ})=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_T\left(i\right)$

(3.2) backward algorithm: the backward variable of definition is:

β _t(i)＝P(O _t+1，O _t+2，…，O _T|Q _t＝q _i，λ)，1≤t≤T-1

In formula: β _t(i)---the probability that observing time, sequence occurred of t+1 moment to last moment under t i state;

(3.2.1) start

β _T(i)＝1，1≤i≤N

(3.2.2) recurrence

${\mathrm{\β}}_t\left(i\right)=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_{\mathrm{ij}}{b}_j\left(O_{t+1}\right){\mathrm{\β}}_{t+1}\left(j\right),1\≤i\≤N,t=T-1,T-2,...,1$

(3.2.3) terminate

$P\left(O\right|\mathrm{\λ})=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\β}}_1\left(i\right)$

Definition according to forward variable and backward variable is derived:

${\mathrm{\ϵ}}_t(i,j)=\frac{{\mathrm{\α}}_t\left(i\right)a_{\mathrm{ij}}{b}_j\left(O_{t+1}\right){\mathrm{\β}}_{t+1}\left(j\right)}{P\left(O\right|\mathrm{\λ})}=\frac{{\mathrm{\α}}_t\left(i\right)a_{\mathrm{ij}}{b}_j\left(O_{t+1}\right){\mathrm{\β}}_{t+1}\left(j\right)}{{\mathrm{\Σ}}_{i=1}^N{\mathrm{\Σ}}_{j=1}^N{\mathrm{\α}}_t\left(i\right)a_{\mathrm{ij}}{b}_j\left(O_{t+1}\right){\mathrm{\β}}_{t+1}\left(j\right)}$

ε _t(i, j)---transfer to the probability of state j in t from state i;

Same derivation obtains t Markov chain and is in q _ishape probability of state is:

${\mathrm{\ϵ}}_t\left(i\right)=P(Q_t=q_i,O|\mathrm{\λ})=\frac{{\mathrm{\α}}_t\left(i\right){\mathrm{\β}}_t\left(i\right)}{{\mathrm{\Σ}}_1^N{\mathrm{\α}}_t\left(i\right){\mathrm{\β}}_t\left(i\right)}=\underset{J=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_t(i,j)$

The revaluation formula of deriving Baum-Welch algorithm is thus as follows:

$\stackrel{\‾}{{\mathrm{\π}}_i}={\mathrm{\ϵ}}_1\left(i\right)$

$\stackrel{\‾}{{\mathrm{\α}}_{\mathrm{ij}}}=\frac{{\mathrm{\Σ}}_{t=1}^{T-1}{\mathrm{\ϵ}}_t(i,j)}{{\mathrm{\Σ}}_{t=1}^{T-1}{\mathrm{\ϵ}}_t\left(i\right)}$

$\stackrel{\‾}{b_j}\left(k\right)=\frac{{\mathrm{\Σ}}_{t=1,O_t=k}^T{\mathrm{\ϵ}}_t\left(j\right)}{{\mathrm{\Σ}}_{t=1}^T{\mathrm{\ϵ}}_t\left(j\right)}$

Be more than the theory introduction in model learning stage, will the roughly flow process obtaining model inner parameter λ locally optimal solution be described below:

First according to number N, the observed value number M of observation sequence determination hidden state, suitable initial model λ is then chosen ₀=(π ₀, A ₀, B ₀); Forward variable α is calculated again according to forward-backward algorithm algorithm _t(i) and backward variable β _t+1j () calculates ε _t(i, j) and ε _t(i); Finally be target by 3 revaluation formula to the maximum with P (O| λ), with carry out loop iteration for the condition of convergence thus obtain the locally optimal solution of model inner parameter λ.

(4) model decode phase: the locally optimal solution being obtained model inner parameter λ by data encasement, data prediction and model learning three phases.Model decode phase adopts Viterbi algorithm on this basis, is obtained the state estimation time series of each remittance vehicle by iteration.Viterbi algorithm specific implementation step is as follows:

(4.1) defining variable δ _t(i)

${\mathrm{\δ}}_t\left(i\right)=\underset{q_1,...,q_{t-1}}{\max }P(q_1,q_2,...,q_t,\mathrm{Qt}=q_i,O_1,O_2,...,O_t|\mathrm{\λ})$

In formula: δ _t(i)---under the condition of setting models λ, along path q ₁, q ₂..., q _tand Q _t=q _itime, export observation sequence O ₁, O ₂..., O _tmaximum probability;

(4.2) define it represents t Q _ithe front and continued state number of state

(4.3) start

δ ₁(i)＝π _ib _i(O ₁)，1≤i≤N

(4.4) recurrence

${\mathrm{\δ}}_t\left(j\right)=\underset{1\≤i\≤N}{\max }\left[{\mathrm{\δ}}_{t-1}\left(i\right)a_{\mathrm{ij}}\right]b_j\left(O_t\right),2\≤t\≤T,1\≤j\≤N$

(4.5) terminate

$P^{*}=\underset{1\≤i\≤N}{\max }\left[{\mathrm{\δ}}_T\left(i\right)\right]$

${q_T}^{*}=\mathrm{ar\; g}\underset{1\≤i\≤N}{\max }\left[{\mathrm{\δ}}_T\left(i\right)\right]$

In formula: arg max---maximize the i value of formula below;

(4.6) optimal estimation status switch

(5) the result treatment stage

(5.1) the driving behavior state for time sequence estimated according to model and initial trace data set can obtain driver and when state transfer occurs, and namely import the start time of decision-making, number of times, the state of the transfer of driving behavior state shift the traffic flow modes information of position coordinates and the corresponding both macro and micro occurred;

(5.2) add up all vehicles import the decision-making moment of main line and then obtain the distribution in decision-making moment, divide dissimilar driver according to its distribution, the expectation value of dissimilar driver's decision-making moment point can be obtained simultaneously;

(5.3) by drawing driver status branch space distribution plan, the place that takes place frequently that driver has lane change to be intended to is found.

Accompanying drawing explanation

Fig. 1 process flow diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing, 1 couple of the present invention is further described.

Embodiment 1:

As shown in Figure 1, a kind of advanced road bottle-neck zone vehicle of the present invention imports behavior method of estimation, comprises the following steps:

(1) data preparation stage: click and enter the remittance process of ring road vehicle as research object using overhead Hong Xu road, Yan'an, Shanghai City bottleneck.Or rather, be research be positioned at that inner side acceleration lane vehicle imports contiguous main line track change decision process.The main line of Hong Xu road bottleneck point has the acceleration lane of three tracks, two treaty 150m length.Sufficiently long acceleration lane is conducive to driver and makes repeatedly decision-making thus select import main line suitable opportunity, and then obtains abundant sample data.First this stage utilizes trajectory extraction software to carry out the extraction of track of vehicle data, then establishes the traffic stream characteristics index set affecting remittance behavior;

(1.1) trajectory extraction software is utilized to carry out the extraction of track of vehicle data, adopt the afterbody center of manual method mouse picking vehicle on the operation interface of software, thus obtain the driving trace of vehicle, through the software inhouse smoothing processing vehicle traveling information time series that finally to obtain with 0.12 second be the time interval.The track data of vehicle comprises the ID of vehicle, moment, the speed of vehicle, the acceleration of vehicle, and the position coordinates of vehicle.By the trajectory extraction to nearly 20 minutes video datas, obtain 32628 track datas altogether, amount to 322 qualified samples;

(1.2) establish the traffic stream characteristics index set C affecting remittance behavior, described traffic stream characteristics index set C comprises the speed V importing vehicle, the acceleration a importing vehicle, imports the time headway T of Adjacent vehicles (front truck, rear car) on vehicle-to-target track _leadand T _lag, import the headstock Ullage S of Adjacent vehicles (front truck, rear car) on vehicle-to-target track _leadand S _lag, import the time headway T of adjacent front truck on vehicle and current lane _prewith headstock Ullage S _pre, import the velocity contrast Δ V of Adjacent vehicles (front truck, rear car) on vehicle-to-target track _leadwith Δ V _lag, and import the position coordinates D of vehicle relative acceleration lane tail end;

(2) data preprocessing phase: this stage comprise traffic stream characteristics index set C data acquisition, import the identification of behavior characteristic variable n, determine the structure R of driving behavior state matrix Q, observable state set, and obtain 3 initial matrixs that originally Hidden Markov Model (HMM) need to input;

(2.1) data acquisition of traffic stream characteristics index set C, according to trajectory extraction software obtain vehicle ID, the moment, the speed of vehicle, the acceleration of vehicle, and the location coordinate information data of vehicle, by indirect calculation obtain Ullage, time apart from, velocity contrast;

Ullage: the Ullage before and after a certain moment between adjacent two cars equals front vehicle position coordinate and deducts the vehicle commander that rear car position coordinates deducts rear car again, unit m;

Time distance: the Ullage before and after current time between adjacent two cars divided by rear car current vehicle speed, unit s;

Velocity contrast: the automobile's instant velocity of current time front truck deducts the speed of a motor vehicle of contiguous rear car, unit m/s;

Vehicle commander's computation rule: compact car 4.5m, in-between car 6.0m, large car 12.0m;

(2.2) import the identification of behavior characteristic variable n, the information that initial set up index set contains is relatively more sufficient, but, these explanatory variables non-fully is remarkable variable.Therefore adopt random forests algorithm to be screened the traffic stream characteristics index set affecting remittance behavior, obtain the characteristic variable affecting remittance behavior.Random forest is a kind of assembled classifier, it utilizes bootstrap repeat replication from original sample, extract multiple sample, each sample is considered as a training set, each training set carries out a decision tree modeling, then these decision trees are combined and certain test sample book is classified, the judged result of every decision tree gathered, the maximum classification results of number of votes obtained is using as the final Output rusults of algorithm.Described characteristic variable n comprise import vehicle acceleration a, import headstock Ullage S between vehicle-to-target track front truck _lead, import time headway T between vehicle-to-target track front truck _lead, import headstock Ullage S between vehicle-to-target track rear car _lag, import velocity contrast Δ V between vehicle-to-target track front truck _lead, and import the velocity contrast Δ V between the rear car of vehicle-to-target track _lag, characteristic variable n as shown in the formula:

n＝(a，S _lead，T _lead，S _lag，ΔV _lead，ΔV _lag)

In formula: a---import the acceleration of vehicle, unit is m/s ²;

S _lead---import the headstock Ullage between the front truck of vehicle-to-target track, unit is m;

T _lead---import the time headway between the front truck of vehicle-to-target track, unit is s;

S _lag---import the headstock Ullage between the rear car of vehicle-to-target track, unit is m;

Δ V _lead---import the velocity contrast between the front truck of vehicle-to-target track, unit is m/s;

Δ V _lag---import the velocity contrast between the rear car of vehicle-to-target track, unit is m/s;

(2.3) determine driving behavior state matrix Q, described state comprises bottle-neck zone and enters the state (remittance state) of ring road vehicle remittance main line and enter ring road vehicle along the normal transport condition of acceleration lane (non-remittance state).

Q＝{q ₁，q ₂}

In formula: q ₁---enter ring road vehicle and import state, represent by numeral 1;

Q ₂---enter ring road vehicle and do not import state, represent by numeral 2;

(2.4) structure of observable state set R, the characteristic variable that step (2.2) obtains is sextuple, and each dimension variable is continuous variable; Owing to needing to carry out sliding-model control to characteristic variable when building Hidden Markov Model (HMM), therefore the interval division such as employing are by a, S _lead, T _lead, S _lag, Δ V _lead, Δ V _lagbe divided into 5 classes, 6 classes, 5 classes, 4 classes, 4 classes and 5 classes respectively.

As mentioned above, the observable state set R that element number is 12000 can finally be obtained.With bidimensional spy amount (S _lead, a) for example illustrates the mode that embodies of observable state set, its mathematical form is as follows:

$\begin{array}{c}R=\{R_{11},...,R_{1j},...,R_{i1},R_{\mathrm{ij}}\}\\ =\left\{\begin{array}{c}(S_{{\mathrm{lead}}_1},a_1),(S_{{\mathrm{lead}}_1},a_2),...,(S_{{\mathrm{lead}}_1},a_k)\\ (S_{{\mathrm{lead}}_2},a_1),({S_{{\mathrm{lead}}_2}}_{},a_2),...,(S_{{\mathrm{lead}}_2},a_k)\\ ......\\ (S_{{\mathrm{lead}}_l},a_1),(S_{{\mathrm{lead}}_l},a_2),...,(S_{{\mathrm{lead}}_l},a_k)\end{array}\right\}\end{array}$

In formula: R _ij---observable state;

A---import the acceleration of vehicle, unit is m/s ²;

S _lead---import the headstock Ullage between the front truck of vehicle-to-target track, unit is m;

L---import the headstock Ullage S between the front truck of vehicle-to-target track _leadaccording to etc. the interval number of interval division, value is 6;

K---the acceleration a importing vehicle according to etc. the interval number of interval division, value is 5;

(2.5) obtain 3 initial matrixs that originally Hidden Markov Model (HMM) needs to input, described initial matrix is state transition probability matrix A, observed value probability distribution matrix B and initial state probabilities distribution matrix π respectively;

State transition probability matrix A: under state transition probability matrix reflects the prerequisite that ring road vehicle previous moment state is determined, subsequent time is certain shape probability of state.As described above obtains the matrix A of 2 × 2, and its mathematical form is as follows:

a _ij＝P(Q _t＝q _j|Q _t-1＝q _i)，i，j＝1 or 2

$A=\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]$

In formula: a _ij---enter ring road vehicle and transfer to another kind of shape probability of state from a kind of state;

A ₁₁---previous moment is remittance state, and a rear moment is for importing shape probability of state;

A ₁₂---previous moment is remittance state, and a rear moment is non-remittance shape probability of state;

A ₂₁---previous moment is non-remittance state, and a rear moment is for importing shape probability of state;

A ₂₂---previous moment is non-remittance state, and a rear moment is non-remittance shape probability of state;

Observed value probability distribution matrix B: it reflects that ring road vehicle (imports or non-remittance) under certain hidden state and is considered to certain observable shape probability of state.Still with two dimensional feature vector (S _lead, a) for example illustrates the form that embodies of observed value probability distribution matrix, its mathematical form is as follows:

b _ij＝P(O _t＝R _ij|Q _t＝q _i)，i＝1 or 2，j＝1，2，…，m

$B=\left[\begin{array}{ccc}{b}_{11}& ...& b_{1m}\\ b_{21}& & b_{2m}\end{array}\right]$

m＝l*k

In formula: b _ij---driver is considered to certain observable shape probability of state under a certain hidden state;

M---all observe the division number of proper vector, the implication of l and k is the same;

Initial state probabilities distribution matrix π: implicit state (importing and the non-remittance) probability distribution matrix when initial time t=1, its mathematical form is as follows:

π＝{π ₁，π ₂}

π ₁＝P ₀(Q _t＝1＝q ₁)

π ₂＝P ₀(Q _t＝1＝q ₂)

In formula: π ₁---during initial time t=1, enter ring road vehicle for importing shape probability of state, value is 1;

π ₂---during initial time t=1, entering ring road vehicle is non-remittance shape probability of state, and value is 0;

(3) the model learning stage: the initial parameter λ to be optimized that can obtain model through data encasement rank and data preprocessing phase ₀, λ ₀=(π, A, B).The model learning stage adopts forward-backward algorithm algorithm constantly to reappraise the parameter lambda of model ₀, after successive ignition, obtain a local optimum parametric solution of model thus provide important leverage tool for the realization of following model decode phase; Body performing step is as follows:

(3.1) forwards algorithms: establish observable state for time sequence O=(O ₁, O ₂..., O _t), O to represent in a vehicle travel process not observable state (characteristic variable value) in the same time, and definition forward variable is:

α _t(i)＝P(O ₁，O ₂，…，O _t，Q _t＝q _i|λ)，1≤t≤T

In formula: α _t(i)---the probability of t hidden state i;

(3.1.1) start

α ₁(i)＝π _ib(O ₁)，t＝1

In formula: b (O ₁)---initial time observer state is O ₁probability;

(3.1.2) recurrence

${\mathrm{\α}}_{t+1}\left(j\right)=\left[\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_t\left(i\right)a_{\mathrm{ij}}\right]b_{{\mathrm{jO}}_{t+1}},1\≤t\≤T-\mathrm{1,1}\≤j\≤N$

In formula: α _t+1j ()---t+1 moment state is the probability of j;

---when hidden state is j, observer state is O _t+1probability;

(3.1.3) terminate

$P\left(O\right|\mathrm{\λ})=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_T\left(i\right)$

(3.2) backward algorithm: the backward variable of definition is:

β _t(i)＝P(O _t+1，O _t+2，…，O _T|Q _t＝q _i，λ)，1≤t≤T-1

In formula: β _t(i)---the probability that observing time, sequence occurred of t+1 moment to last moment under t i state;

(3.2.1) start

β _T(i)＝1，1≤i≤N

(3.2.2) recurrence

${\mathrm{\β}}_t\left(i\right)=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_{\mathrm{ij}}{b}_j\left(O_{t+1}\right){\mathrm{\β}}_{t+1}\left(j\right),1\≤i\≤N,t=T-1,T-2,...,1$

(3.2.3) terminate

$P\left(O\right|\mathrm{\λ})=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\β}}_1\left(i\right)$

Definition according to forward variable and backward variable is derived:

${\mathrm{\ϵ}}_t(i,j)=\frac{{\mathrm{\α}}_t\left(i\right)a_{\mathrm{ij}}{b}_j\left(O_{t+1}\right){\mathrm{\β}}_{t+1}\left(j\right)}{P\left(O\right|\mathrm{\λ})}=\frac{{\mathrm{\α}}_t\left(i\right)a_{\mathrm{ij}}{b}_j\left(O_{t+1}\right){\mathrm{\β}}_{t+1}\left(j\right)}{{\mathrm{\Σ}}_{i=1}^N{\mathrm{\Σ}}_{j=1}^N{\mathrm{\α}}_t\left(i\right)a_{\mathrm{ij}}{b}_j\left(O_{t+1}\right){\mathrm{\β}}_{t+1}\left(j\right)}$

In formula: ε _t(i, j)---transfer to the probability of state j in t from state i;

Same derivation obtains t Markov chain and is in q _ishape probability of state is:

${\mathrm{\ϵ}}_t\left(i\right)=P(Q_t=q_i,O|\mathrm{\λ})=\frac{{\mathrm{\α}}_t\left(i\right){\mathrm{\β}}_t\left(i\right)}{{\mathrm{\Σ}}_1^N{\mathrm{\α}}_t\left(i\right){\mathrm{\β}}_t\left(i\right)}=\underset{J=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_t(i,j)$

The revaluation formula of deriving Baum-Welch algorithm is thus as follows:

$\stackrel{\‾}{{\mathrm{\π}}_i}={\mathrm{\ϵ}}_1\left(i\right)$

$\stackrel{\‾}{{\mathrm{\α}}_{\mathrm{ij}}}=\frac{{\mathrm{\Σ}}_{t=1}^{T-1}{\mathrm{\ϵ}}_t(i,j)}{{\mathrm{\Σ}}_{t=1}^{T-1}{\mathrm{\ϵ}}_t\left(i\right)}$

$\stackrel{\‾}{b_j}\left(k\right)=\frac{{\mathrm{\Σ}}_{t=1,O_t=k}^T{\mathrm{\ϵ}}_t\left(j\right)}{{\mathrm{\Σ}}_{t=1}^T{\mathrm{\ϵ}}_t\left(j\right)}$

Be more than the theory introduction in model learning stage, will the roughly flow process obtaining model inner parameter λ locally optimal solution be described below:

First according to number N, the observed value number M of observation sequence determination hidden state, suitable initial model λ is then chosen ₀=(π ₀, A ₀, B ₀); Forward variable α is calculated again according to forward-backward algorithm algorithm _t(i) and backward variable β _t+1j () calculates ε _t(i, j) and ε _t(i); Finally be target by 3 revaluation formula to the maximum with P (O| λ), with carry out loop iteration for the condition of convergence thus obtain the locally optimal solution of model inner parameter λ.

(4) model decode phase: the locally optimal solution being obtained model inner parameter λ by data encasement, data prediction and model learning three phases.Model decode phase adopts Viterbi algorithm on this basis, is obtained the state estimation time series of each remittance vehicle by iteration.Viterbi algorithm specific implementation step is as follows:

(4.1) defining variable δ _t(i)

${\mathrm{\δ}}_t\left(i\right)=\underset{q_1,...,q_{t-1}}{\max }P(q_1,q_2,...,q_t,\mathrm{Qt}=q_i,O_1,O_2,...,O_t|\mathrm{\λ})$

In formula: δ _t(i)---under the condition of setting models λ, along path q ₁, q ₂..., q _tand Q _t=q _itime, export observation sequence O ₁, O ₂..., O _tmaximum probability;

(4.2) define it represents t Q _ithe front and continued state number of state

(4.3) start

δ ₁(i)＝π _ib _i(O ₁)，1≤i≤N

(4.4) recurrence

${\mathrm{\δ}}_t\left(j\right)=\underset{1\≤i\≤N}{\max }\left[{\mathrm{\δ}}_{t-1}\left(i\right)a_{\mathrm{ij}}\right]b_j\left(O_t\right),2\≤t\≤T,1\≤j\≤N$

(4.5) terminate

$P^{*}=\underset{1\≤i\≤N}{\max }\left[{\mathrm{\δ}}_T\left(i\right)\right]$

${q_T}^{*}=\mathrm{ar\; g}\underset{1\≤i\≤N}{\max }\left[{\mathrm{\δ}}_T\left(i\right)\right]$

In formula: arg max---maximize the i value of formula below;

(4.6) optimal estimation status switch

(5) the result treatment stage

(5.1) the driving behavior state for time sequence estimated according to model and initial trace data set can obtain driver and when state transfer occurs, and namely import the start time of decision-making, number of times, the state of the transfer of driving behavior state shift the traffic flow modes information of position coordinates and the corresponding both macro and micro occurred;

(5.2) add up all vehicles import the decision-making moment of main line and then obtain the distribution in decision-making moment, divide dissimilar driver according to its distribution, the expectation value of dissimilar driver's decision-making moment point can be obtained simultaneously;

(5.3) by drawing driver status branch space distribution plan, the place that takes place frequently that driver has lane change to be intended to is found.

Claims (1)

1. an advanced road bottle-neck zone vehicle imports behavior method of estimation, it is characterized in that: the method utilizes Hidden Markov Model (HMM) to estimate the decision situation in driver's remittance process, comprise data preparation stage, data preprocessing phase, model learning stage, model decode phase and result treatment double teacher, concrete steps are as follows:

(1) data preparation stage: first utilize trajectory extraction software to carry out the extraction of track of vehicle data, then establishes the traffic stream characteristics index set affecting remittance behavior;

(1.1) utilize trajectory extraction software to carry out the extraction of track of vehicle data, the track data of vehicle comprises the ID of vehicle, moment, the speed of vehicle, the acceleration of vehicle, and the position coordinates of vehicle;

(1.2) establish the traffic stream characteristics index set C affecting remittance behavior, described traffic stream characteristics index set C comprises the speed V importing vehicle, the acceleration a importing vehicle, imports the time headway T of Adjacent vehicles (front truck, rear car) on vehicle-to-target track _leadand T _lag, import the headstock Ullage S of Adjacent vehicles (front truck, rear car) on vehicle-to-target track _leadand S _lag, import the time headway T of adjacent front truck on vehicle and current lane _prewith headstock Ullage S _pre, import the velocity contrast Δ V of Adjacent vehicles (front truck, rear car) on vehicle-to-target track _leadwith Δ V _lag, and import the position coordinates D of vehicle relative acceleration lane tail end;

(2) data preprocessing phase: this stage comprise traffic stream characteristics index set C data acquisition, import the identification of behavior characteristic variable n, determine the structure R of driving behavior state matrix Q, observable state set, and obtain 3 initial matrixs that originally Hidden Markov Model (HMM) need to input;

(2.1) data acquisition of traffic stream characteristics index set C, according to trajectory extraction software obtain vehicle ID, the moment, the speed of vehicle, the acceleration of vehicle, and the location coordinate information data of vehicle, by indirect calculation obtain Ullage, time apart from, velocity contrast;

Ullage: the Ullage before and after a certain moment between adjacent two cars equals front vehicle position coordinate and deducts the vehicle commander that rear car position coordinates deducts rear car again, unit m;

Time distance: the Ullage before and after current time between adjacent two cars divided by rear car current vehicle speed, unit s;

Velocity contrast: the automobile's instant velocity of current time front truck deducts the speed of a motor vehicle of contiguous rear car, unit m/s;

Vehicle commander's computation rule: compact car 4.5m, in-between car 6.0m, large car 12.0m;

(2.2) import the identification of behavior characteristic variable n, adopt random forests algorithm to be screened the traffic stream characteristics index set affecting remittance behavior, obtain the characteristic variable affecting remittance behavior; Described characteristic variable comprise import vehicle acceleration a, import headstock Ullage S between vehicle-to-target track front truck _lead, import time headway T between vehicle-to-target track front truck _lead, import headstock Ullage S between vehicle-to-target track rear car _lag, import velocity contrast Δ V between vehicle-to-target track front truck _lead, and import the velocity contrast Δ V between the rear car of vehicle-to-target track _lag, characteristic variable n as shown in the formula:

n＝(a，S _lead，T _lead，S _lag，ΔV _lead，ΔV _lag)

In formula: a---import the acceleration of vehicle, unit is m/s ²;

S _lead---import the headstock Ullage between the front truck of vehicle-to-target track, unit is m;

T _lead---import the time headway between the front truck of vehicle-to-target track, unit is s;

S _lag---import the headstock Ullage between the rear car of vehicle-to-target track, unit is m;

Δ V _lead---import the velocity contrast between the front truck of vehicle-to-target track, unit is m/s;

Δ V _lag---import the velocity contrast between the rear car of vehicle-to-target track, unit is m/s;

(2.3) determine driving behavior state matrix Q, described state comprises bottle-neck zone and enters the state (remittance state) of ring road vehicle remittance main line and enter ring road vehicle along the normal transport condition of acceleration lane (non-remittance state);

Q＝{q ₁，q ₂}

In formula: q ₁---enter ring road vehicle and import state, represent by numeral 1;

Q ₂---enter ring road vehicle and do not import state, represent by numeral 2;

(2.4) structure of observable state set R, the characteristic variable that step (2.2) obtains is sextuple, and each dimension variable is continuous variable; Owing to needing to carry out sliding-model control to characteristic variable when building Hidden Markov Model (HMM), therefore the interval division such as employing are by a, S _lead, T _lead, S _lag, Δ V _lead, Δ V _lagbe divided into k class, l class, p class, s class, h class and z class respectively; As mentioned above, the observable state set R that element number is k × l × p × s × h × z is finally obtained, with two dimensional feature vector (S _lead, a) for example illustrates the mode that embodies of observable state set R, its mathematical form is as follows:

$\begin{array}{c}R=\{R_{11},...,R_{1j},...,R_{i1},R_{\mathrm{ij}}\}\\ =\left\{\begin{array}{c}(S_{{\mathrm{lead}}_1},a_1),(S_{{\mathrm{lead}}_1},a_2),...,(S_{{\mathrm{lead}}_1},a_k)\\ (S_{{\mathrm{lead}}_2},a_1),(S_{{\mathrm{lead}}_2},a_2),...,(S_{{\mathrm{lead}}_2},a_k)\\ ......\\ (S_{{\mathrm{lead}}_l},a_1),(S_{{\mathrm{lead}}_l},a_2),...,(S_{{\mathrm{lead}}_l},a_k)\end{array}\right\}\end{array}$

In formula: R _ij---observable state;

A---import the acceleration of vehicle, unit is m/s ²;

S _lead---import the headstock Ullage between the front truck of vehicle-to-target track, unit is m;

L---import the headstock Ullage S between the front truck of vehicle-to-target track _leadaccording to etc. the interval number of interval division;

K---the acceleration a importing vehicle according to etc. the interval number of interval division;

(2.5) obtain 3 initial matrixs that originally Hidden Markov Model (HMM) needs to input, described initial matrix is state transition probability matrix A, observed value probability distribution matrix B and initial state probabilities distribution matrix π respectively;

State transition probability matrix A: state transition probability matrix reflection be that under the prerequisite determined of ring road vehicle previous moment state, subsequent time is certain shape probability of state; As described above obtains the matrix A of 2 × 2, and its mathematical form is as follows:

a _ij＝P(Q _t＝q _j|Q _t-1＝q _i)，i，j＝1or2

$A=\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]$

In formula: a _ij---enter ring road vehicle and transfer to another kind of shape probability of state from a kind of state;

A ₁₁---previous moment is remittance state, and a rear moment is for importing shape probability of state;

A ₁₂---previous moment is remittance state, and a rear moment is non-remittance shape probability of state;

A ₂₁---previous moment is non-remittance state, and a rear moment is for importing shape probability of state;

A ₂₂---previous moment is non-remittance state, and a rear moment is non-remittance shape probability of state;

Observed value probability distribution matrix B: it reflects that ring road vehicle (imports or non-remittance) under certain hidden state and is considered to certain observable shape probability of state; Still with two dimensional feature vector (S _lead, a) for example illustrates the form that embodies of observed value probability distribution matrix B, its mathematical form is as follows:

b _ij＝P(O _t＝R _ij|Q _t＝q _i)，i=1or2，j＝1，2，…，m

$B=\left[\begin{array}{ccc}{b}_{11}& ...& b_{1m}\\ b_{21}& ...& b_{2m}\end{array}\right]$

m＝l*k

In formula: b _ij---driver is considered to certain observable shape probability of state under a certain hidden state;

M---all observe the division number of proper vector, the implication of l and k is the same;

Initial state probabilities distribution matrix π: implicit state (importing and the non-remittance) probability distribution matrix when initial time t=1, its mathematical form is as follows:

π＝{π ₁，π ₂}

π ₁＝P ₀(Q _t＝1＝q ₁)

π ₂＝P ₀(Q _t＝1＝q ₂)

In formula: π ₁---during initial time t=1, enter ring road vehicle for importing shape probability of state;

π ₂---during initial time t=1, entering ring road vehicle is non-remittance shape probability of state;

(3) the model learning stage: the initial parameter λ to be optimized that can obtain model through data preparation stage and data preprocessing phase ₀, λ ₀=(π, A, B); The model learning stage adopts forward-backward algorithm algorithm constantly to reappraise the parameter lambda of model ₀, after successive ignition, obtain a local optimum parametric solution of model thus provide important leverage for the realization of following model decode phase; Specific implementation step is as follows:

(3.1) forwards algorithms: establish observable state for time sequence O=(O ₁, O ₂..., O _t), O to represent in a vehicle travel process not observable state (characteristic variable value) in the same time, and definition forward variable is:

α _t(i)＝P(O ₁，O ₂，…，O _t，Q _t＝q _i|λ)，1≤t≤Ｔ

In formula: α _t(i)---the probability of t hidden state i;

(3.1.1) start

α ₁(i)＝π _ib(O ₁)，t＝1

In formula: b (O ₁)---initial time observer state is O ₁probability;

(3.1.2) recurrence

${\mathrm{\α}}_{t+1}\left(j\right)=\left[\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_t\left(i\right)a_{\mathrm{ij}}\right]b_{j{O}_{t+1}},1\≤t\≤T-\mathrm{1,1}\≤j\≤N$

In formula: α _t+1j ()---t+1 moment state is the probability of j;

---when hidden state is j, observer state is O _t+1probability;

(3.1.3) terminate

$P\left(O\right|\mathrm{\λ})=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_T\left(i\right)$

(3.2) backward algorithm: the backward variable of definition is:

β _t(i)＝P(O _t+1，O _t+2，…，O _T|Q _t＝q _i，λ)，1≤t≤T-1

In formula: β _t(i)---from the t+1 moment to the probability that the observing time of last moment, sequence occurred under t i state;

(3.2.1) start

β _T(i)＝1，1≤i≤N

(3.2.2) recurrence

${\mathrm{\β}}_t\left(i\right)=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_{\mathrm{ij}}{b}_j\left(O_{t+1}\right){\mathrm{\β}}_{t+1}\left(j\right),1\≤i\≤N,t=T-1,T-2,...,1$

(3.2.3) terminate

$P\left(O\right|\mathrm{\λ})=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\β}}_1\left(i\right)$

Definition according to forward variable and backward variable is derived:

${\mathrm{\ϵ}}_t(i,j)=\frac{{\mathrm{\α}}_t\left(i\right)a_{\mathrm{ij}}{b}_j\left(O_{t+1}\right){\mathrm{\β}}_{t+1}\left(j\right)}{P\left(O\right|\mathrm{\λ})}=\frac{{\mathrm{\α}}_t\left(i\right)a_{\mathrm{ij}}{b}_j\left(O_{t+1}\right){\mathrm{\β}}_{t+1}\left(j\right)}{{\mathrm{\Σ}}_{i=1}^N{\mathrm{\Σ}}_{j=1}^N{\mathrm{\α}}_t\left(i\right)a_{\mathrm{ij}}{b}_j\left(O_{t+1}\right){\mathrm{\β}}_{t+1}\left(j\right)}$

In formula: ε _t(i, j)---transfer to the probability of state j in t from state i;

Same derivation obtains t Markov chain and is in q _ishape probability of state is:

${\mathrm{\ϵ}}_t\left(i\right)=P(Q_t=q_i,O|\mathrm{\λ})=\frac{{\mathrm{\α}}_t\left(i\right){\mathrm{\β}}_t\left(i\right)}{{\mathrm{\Σ}}_1^N{\mathrm{\α}}_t\left(i\right){\mathrm{\β}}_t\left(i\right)}=\underset{J=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_t(i,j)$

The revaluation formula of deriving Baum-Welch algorithm is thus as follows:

$\stackrel{\‾}{{\mathrm{\π}}_i}={\mathrm{\ϵ}}_1\left(i\right)$

$\stackrel{\‾}{{\mathrm{\α}}_{\mathrm{ij}}}=\frac{{\mathrm{\Σ}}_{t=1}^{T-1}{\mathrm{\ϵ}}_t(i,j)}{{\mathrm{\Σ}}_{t=1}^{T-1}{\mathrm{\ϵ}}_t\left(i\right)}$

$\stackrel{\‾}{b_j}\left(k\right)=\frac{{\mathrm{\Σ}}_{t=1,O_t=k}^T{\mathrm{\ϵ}}_t\left(j\right)}{{\mathrm{\Σ}}_{t=1}^T{\mathrm{\ϵ}}_t\left(j\right)}$

The flow process obtaining model inner parameter λ locally optimal solution is:

First according to number N, the observed value number M of observation sequence determination hidden state, suitable initial model λ is then chosen ₀=(π ₀, A ₀, B ₀); Forward variable α is calculated again according to forward-backward algorithm algorithm _t(i) and backward variable β _t+1j () calculates ε _t(i, j) and ε _t(i); Finally be target by 3 revaluation formula to the maximum with P (O| λ), with carry out loop iteration for the condition of convergence thus obtain the locally optimal solution of model inner parameter λ;

(4) model decode phase: model decode phase adopts Viterbi algorithm, is obtained the state estimation time series of each remittance vehicle by iteration; Viterbi algorithm specific implementation step is as follows:

(4.1) defining variable δ _t(i)

${\mathrm{\δ}}_t\left(i\right)=\underset{q_1,...,q_{t-1}}{\max }P(q_1,q_2,...,q_t,Q_t=q_i,O_1,O_2,...,O_t|\mathrm{\λ})$

In formula: δ _t(i)---under the condition of setting models λ, along path q ₁, q ₂..., q _tand Q _t=q _ttime, export observation sequence O ₁, O ₂..., O _tmaximum probability;

(4.2) define it represents t Q _ithe front and continued state number of state

(4.3) start

δ ₁(i)＝π _ib _i(O ₁)，1≤i≤Ｎ

(4.4) recurrence

${\mathrm{\δ}}_t\left(j\right)=\underset{1\≤i\≤N}{\max }\left[{\mathrm{\δ}}_{t-1}\left(i\right)a_{\mathrm{ij}}\right]b_j\left(O_t\right),2\≤t\≤T,1\≤j\≤N$

(4.5) terminate

$P^{*}=\underset{1\≤i\≤N}{\max }\left[{\mathrm{\δ}}_T\left(i\right)\right]$

${q_T}^{*}=\arg \underset{1\≤i\≤N}{\max }\left[{\mathrm{\δ}}_T\left(i\right)\right]$

In formula: arg max---maximize the i value of formula below;

(4.6) optimal estimation status switch

(5) the result treatment stage

(5.1) the driving behavior state for time sequence estimated according to model and initial trace data set can obtain driver and when state transfer occurs, and namely import the start time of decision-making, number of times, the state of the transfer of driving behavior state shift the position coordinates and corresponding both macro and micro traffic flow modes information that occur;

(5.2) add up all vehicles import the decision-making moment of main line and then obtain the distribution in decision-making moment, divide dissimilar driver according to its distribution, the expectation value of dissimilar driver's decision-making moment point can be obtained simultaneously;

(5.3) by drawing driver status branch space distribution plan, the place that takes place frequently that driver has lane change to be intended to is found.